1. Field of the Invention
This invention relates generally to accelerometers and more particularly to micromachined accelerometers using digital feedback.
2. Description of the Related Art
Accelerometers are sensors that measure acceleration. Accelerometers can be designed to measure rotational or translational acceleration, as well as Coriolis acceleration in a vibratory rate gyroscope. Accelerometers have uses in many commercial, military, and scientific applications including, but not limited to, inertial navigation, vehicular safety systems such as airbags, ride comfort control, platform stabilization, tilt sensing, and vibration monitoring.
The heart of an accelerometer is a mechanical proof-mass. The proof-mass is connected to a substrate by a suspension. Under an applied acceleration, the proof-mass moves with respect to the substrate. It may be shown that for frequencies below the proof-mass resonant frequency along the sensitive axis, xcfx89n, the displacement of the proof-mass from its nominal position with respect to the substrate is given by 1/xcfx89n2 times the applied acceleration. By measuring the displacement of the proof-mass with an electrical interface, acceleration may be inferred.
A sense-element may be operated either open-loop, or placed into a force-feedback loop. Enclosure of a sense-element in a force-feedback loop is commonly called force-balancing or force-rebalancing. In the open-loop configuration, the accelerometer output is given by the change in displacement of the proof-mass multiplied by the gain of the position sense interface. Often piezoelectric materials, piezoresistive materials, or air-gap capacitors are used in conjunction with an electrical position-sense interface to detect proof-mass displacements. In the force-balanced configuration the position-sense interface output is used to feed back a force in a manner that tends to restore the proof-mass to a defined nominal position. Air-gap capacitors or piezoelectric materials are often used to apply feedback forces to the proof mass. In a force-balanced configuration the accelerometer output is not a position, but rather is a quantity representative of the force necessary to keep the proof mass at its nominal position. Closed-loop operation may provide several advantages that are particularly important for miniature micromachined sensors including improved linearity, increased dynamic range, and extended bandwidth. In addition, since the output is the applied force, not displacement, the output typically is less sensitive to device dimensions, such as spring width, making the sensor typically less sensitive to variations in manufacturing.
While there are many ways of implementing a feedback loop, force-feedback with discrete (or digital) levels is particularly attractive because it is simple, provides a digital output, and can be easily implemented in modern integrated microelectronic technologies, thereby enabling co-fabrication of signal processing circuitry with an accelerometer on a single substrate.
Digital feedback is commonly used in analog-to-digital (A/D) voltage converters. The design of A/D voltage converters using digital feedback is well understood by those skilled in the art, with many comprehensive references available on the subject (For example Norsworthy, et al., Delta-Sigma Data Converters, IEEE Press, Piscataway, N.J., 1997; Candy, et al., Oversampling Delta-Sigma Data Converters, IEEE Press, Piscataway, N.J., 1992). A class of these converters is commonly known as sigma-delta or delta-sigma converters. A block diagram of a typical sigma-delta A/D voltage converter with a digital feedback loop having second-order loop filter dynamics is shown in FIG. 1. A one-bit quantizer is used for analog-to-digital (A/D) conversion at the second integrator output. The one-bit signal is fed back to summing nodes at both the converter input, at node N1, and the internal node N2. Feedback to the internal node stabilizes closed-loop dynamics. By taking the output of the modulator as the one-bit quantizer output, analog-to-digital conversion is achieved. When an input signal is applied to the converter, the one-bit digital feedback is subtracted from the input and the resulting error, e, integrated. Assuming the feedback loop is properly compensated, the negative feedback drives the average of the error, e, over many periods to zero causing the average output to track the input. The feedback loop is operated at a sampling rate fs typically many times faster than the Nyquist rate of the input signal fN, enabling a moving average of the output to be constructed at the Nyquist rate. By digitally filtering, or averaging, the digital output, the one-bit data stream is converted to a multi-bit digital signal at a lower bandwidth.
While sigma-delta converters can provide numerous advantages over other topologies, including improved linearity and high dynamic range, they are subject to limit cycles, tones, and deadbands caused by the dynamics of the nonlinear feedback loop. These tones, deadbands, and limit cycles may be input-level dependent and can impede construction of an accurate digital signal from the analog input. Several techniques are known to attenuate these effects in analog-to-digital voltage converters including: high-order loop filters, unstable loop filters, nonsubtractive dithering, filtered or shaped dithering, and subtractive dithering. In subtractive dithering, a dither voltage is often applied to the quantizer input. The dither voltage is controlled by a random or pseudorandom noise generator, and may be digitally subtracted from the converter output. Effective subtractive dithering requires that the voltage applied to the input of the converter be precisely controlled so that it may be removed from the output of the converter.
A mechanical mass may be used as a second order loop-filter in an A/D converter where the analog input quantity is acceleration. The proof-mass integrates acceleration, or an equivalent inertial force, twice to position for frequencies above its resonance. A position-sense interface measures the displacement of the proof-mass from its nominal position. There are many position-sense interface topologies and techniques well known by those skilled in the art (See, for example: Smith, T., et al., xe2x80x9cA 15b electromechanical sigma-delta converter for acceleration measurements,xe2x80x9d IEEE International Solid-State Circuits Conference, 1994, pp. 160-1; Lu, et al., xe2x80x9cA monolithic surface micromachined accelerometer with digital output,xe2x80x9d IEEE J. Solid-State Circuits, December 1995, pp. 1367-73; Lemkin, Micro Accelerometer Design with Digital Feedback Control, Doctoral Thesis, U.C. Berkeley, Fall 1997; Lemkin, et al., xe2x80x9cA three-axis micromachined accelerometer with a CMOS position-sense interface and digital offset-trim electronics,xe2x80x9d IEEE J. Solid-State Circuits, April 1999, pp. 456-68; U.S. Pat. No. 4,345,474, Aug. 24, 1982, Deval; U.S. Pat. No. 4,679,434, Jul. 14, 1987, Stewart; U.S. Pat. No. 4,736,629, Apr. 12, 1988, Cole; U.S. Pat. No. 4,922,756, May 8, 1990, Henrion; U.S. Pat. No. 5,115,291, May 19, 1992, Stokes; U.S. Pat. No. 5,343,766, Sep. 6, 1994, Lee; U.S. Pat. No. 5,345,824, Sep. 13, 1994, Sherman, et al.; U.S. Pat. No. 5,473,946, Dec. 12, 1995, Wyse, et al.; U.S. Pat. No. 5,511,420, Apr. 30, 1996, Zhao, et al.; U.S. Pat. No. 5,540,095, Jul. 30, 1996, Sherman, et al.; U.S. Pat. No. 5,600,066, Feb. 4, 1997, Torregrosa; U.S. Pat. No. 5,635,638, Jun. 3, 1997, Geen; U.S. Pat. No. 5,992,233, Nov. 30, 1999, Clark; U.S. Pat. No. 6,035,694, Mar. 14, 2000, Dupuie, et al.)
A one-bit quantizer converts the output of the position sense interface into a digital value used for feedback. This value is also taken as the output. Unfortunately, it is impossible to directly obtain the stabilizing inner feedback loop shown in FIG. 1 because there is no way to directly input a velocity to a mechanical system.
A discrete-time Finite Impulse Response (FIR) filter may be used to provide phase lead for stable operation. By using a filter, positive phase may be added only where needed, thereby keeping a majority of the second order noise shaping characteristics of the mechanical system. Note that a 2-tap FIR filter will stabilize the feedback loop. A 2-tap FIR filter is a discrete-time finite difference equation of the form:
Out(kT)=Au(kT)+Bu((kxe2x88x921)T)xe2x80x83xe2x80x83Eq. 1
where A and B are constants, T is the sample interval, and k is the sample number. The above equation is discrete-time, but in this general form the filter inputs and outputs are still analog, not digital.
The compensator may be placed either in the analog domain (before the quantizer) or in the digital domain (after the quantizer). In practice, placing the compensator in the feedback path often reduces system linearity, since a multi-bit digital-to-analog voltage converter (DAC) is needed for conversion of the digital feedback signal to an analog voltage.
A digital accelerometer with improved transfer characteristics. In one embodiment of the invention, subtractive dithering is used to attenuate dead zones and input-output nonlinearities arising, in part, from a nonzero resonant frequency of the proof-mass. The disclosed invention is advantageous because dither force may be directly applied to the mechanical proof-mass utilizing electrostatic structures similar to electrostatic structures used for force-feedback. The electrostatic dithering structures provide good matching between the feedback and dither electrodes, enabling effective subtraction of the dither signal from the accelerometer output.